A doubt regarding vectors, scalars and their role in physics

[JackFyre]

TL;DR Summary

A doubt regarding vectors, scalars and their role in physics

I have a doubt regarding the basic function of vectors and scalars in physics-

What is the guarantee that every quantity(measured) in physics can be classified as either a vector or a scalar, and that while performing operations on said quantities, they will obey the already established rules of vector/scalar operations?

 

[Arjan82]

What is the guarantee that every quantity(measured) in physics can be classified as either a vector or a scalar, and that while performing operations on said quantities, they will obey the already established rules of vector/scalar operations?

zero... zero guarantees... It just seems to do quite alright considering what we've achieved by using them. What do you suggest as alternative?

 

[PeroK]

Summary:: A doubt regarding vectors, scalars and their role in physics

I have a doubt regarding the basic function of vectors and scalars in physics-

What is the guarantee that every quantity(measured) in physics can be classified as either a vector or a scalar, and that while performing operations on said quantities, they will obey the already established rules of vector/scalar operations?

Can you be more precise about your question?

It's generally implied in classical physics that if we have two particles of mass $m_1$ and $m_2$ and we put them together, then we have a system of mass $m = m_1 + m_2$.

There's no guarantee that will be correct. It's more an axiom or postulate of classical mechanics that gets tested (along with all the other axioms, postulates or laws of motion) during an experiment.

And, in fact, in relativistic mechanics if $m$ above represents rest mass, then it's not true. For example, if $m_e$ is the mass of an electron and $m_p$ the mass of a proton, and $m$ is the mass of a hydrogen atom with one proton and one electron, then: $m \ne m_p + m_e$.

 

[JackFyre]

Can you be more precise about your question?

It's generally implied in classical physics that if we have two particles of mass $m_1$ and $m_2$ and we put them together, then we have a system of mass $m = m_1 + m_2$.

There's no guarantee that will be correct. It's more an axiom or postulate of classical mechanics that gets tested (along with all the other axioms, postulates or laws of motion) during an experiment.

And, in fact, in relativistic mechanics if $m$ above represents rest mass, then it's not true. For example, if $m_e$ is the mass of an electron and $m_p$ the mass of a proton, and $m$ is the mass of a hydrogen atom with one proton and one electron, then: $m \ne m_p + m_e$.

That pretty much answers it, thanks!

 

[Chestermiller]

Scalars and vectors are just zero- and first order tensors, respectively. In physics and engineering we also need to employ higher order tensors, such as the stress tensor.